Computing chart



C. B. SMITH. i COMPUTING CHART.` APPLICATION man Aus.12.1921.

Patented Jan. 10, 1922'. I

w n m m PATENT OFFICE.

CEDRIC B. SMITH, 0F CHICAGO, ILLINOIS.

COMPUTING cnam?.

Application filed August 12, 1921.

To all 'whom t may concern:

Be it known that I, CEDRIC B. SMITH, a citizen of the United States, residing at Chicago, in the county of Cook and State of Illinois, have invented certain new and useful Improvements in Computing Charts, of which the following is a specification.

My invention relates to improvements in computing charts and has particular reference to means for graphically determining an unknown quantity from a given value of a known quantity, the relative values of which are controlled by two or more factors.

The principal objects of my invention are to provide an improved chart of the general character specified which chart may be readily used by the unskilled or by those having little knowledge of mathematics; to

provide a chart which shall be well within the limits of practical accuracy for the work intended; to provide a chart which may readily be adapted for different scales and which may be suited to a wide range of usefulness, and in general to provide an improved eiiicient computing chart of the character referred to.

In the drawing I have illustrated my invention as applied to a chart for graphically determining or computing advertising cost per unit of space per unit of circulation. In said drawing the ligure is a plan view of said chart.

Referring to the drawing, it will be observed that the area of the chart is inscribed with two sets of parallel guide lines, in the present instance one set being horizontal and the other set being vertical. The horizontal guide lines 10 in this case perform a double function of serving as guide lines both for the known 'quantity values and for the unknown quantity values which arc` to be determined. l

In the particular embodiment shown the known values, at the left of the chart, which represent costs in dollars perpissue per page of advertising ina daily, weekly, monthly orl other publication, range from zero at the top of the scale to $500 at the bottom of the scale, the intermediate values being uniformly spaced according to an arithmetical progression `and according to the uniform spacing of the parallel kguide lines 10.

,The unknown value scale is arranged at the right hand side of the chart and in the present case represents cost per line per million circulation, which is a standard unit in the publishing` business for comparing Specification of Letters latent.

Patented Jan. 10, 1922.

Serial No. 491,674.

advertising costs. These values of unit cost are also arranged in a regular arithmetical progression and for convenience are spaced to correspond with the spacing of the uniformly spaced horizontal guide lines 10. It will beobserved that the zero of the unknown quantity scale is diagonally opposite to the zero of the known quantity scale at the left of the chart.

The cost per standard unit of advertising where the cost per page is known is determined or controlled in accordance with the circulation of the periodical and the number of lines in, or pagesize of, the periodical. In view of the fact that a standard line is 1/14 of an inch in height and usually very close to 2 inches in length, a line is ordinarily considered to be a standard measurement of the advertising area. Hence, if the net length or depth of the page of the periodical and the number of columns he known, it is a simple matter to compute the number of lines for a page. In practicing my invention this computation is not required for the reason that I may employ curves or lines which actually represent, and are designated by, the sizes of pages ordinarily used for periodical purposes. For instance, A41 would represent a page of one-column width having a net space depth of four inches and a line designated C-11 would represent a three-column page eleven inches in depth. It may also be convenient vto have additional lines or curves represent- 'ing even hundreds of lines.

The curves 11 which represent page sizes or quant-ities of lines are in the present instance straight and all, converge towards a common origin or focus 12 which intersects the horizontal guide line 13 corresponding with the zero value of page cost. It will be noticed that said page size curves are inscribed on the chart in such a way as to intersect the page cost guide lines 10.

Somewhat similar curves 14k are inscribed on the chart to represent circulation or number of readers and said lines extend upwardly from a common focus or origin 15, which origin is intersected by the guide line 16 representing zero cost per standard unit of advertising, i. e., cost per line per million circulation. These circulation value lines extend upwardly from the origin 15 and also intersect the guide lines 10 repre-V senting page cost and unit cost. In view of the fact that a smaller page size makes the advertising per unit more expensive, it will llO be seen that the page size curves are arranged in a descending: positive progression, whereas the unit cost scale is arranged in an ascending positive progression. Also since high circulation reduces the advertising cost perv unit, the highervalues of circulation are represented by the circulationcurves which v are closer to the origin line 16 than the cir-V culation lines of less value. Y

The chart is used as follows. Assume that Vthe advertiser is quoted a price of $160. yper vpage and is advisedthat the page size of the vparticular publication is question is B-Q,

thatis yto say, two columns each Vnine'inches in depth, and that the'circulation is 20,000. To determine the cost per line ,per million circulation, which is the standard unit employed vfor :comparing advertising costs, a

'line 1T is drawn horizontally from the-value $160 on a page-cost .scale until it intersects the curve designated `B4) (252 lines). Erom 'Y said intersection a line 18 is then dravvn yto vertically: or at-iight angles to the $160 line 1-7 until lsaid vertical -line 18 intersects the circulation curve designated 20,000. From said point-of,intersectiona line 19 is then drawn horizontally `to intersect the lright hand or costTper-unit scale,they point of said last intersection correspondingto the standard unit cost-Which `was tobe determine Y being inthe stated example .$31.74.

The horizontal guide; lines A10 and the sets Vof vertical guide-lines 20 -are inscribed' on Will be understood that ytheiscoperof the invention should Vbe `determinedrrby the appended claims, said 'claims fbeing 'construed as broadly as possible `consistent,iviththe stateof theart. Y. o

lrclaimas my invention:

1. Acomputing device comprising ashcet having inscribed thereon a scaleofdiiieient values of a `known quantity uniformlyspaced according to 1an" ai'ithinetical progression, V a series of curves each representinga different value of a known factor and capable'of being iiitersected byja setofjparallelllines `draiv'n from-said knownquantity values, a scale of unknown b quantity values also [uniformly spaced according toran;arithmeticalprogression andto which Ya seriesof parallel f'lines may he drawn, Yacres,Sir-.the sheet; and: another series of curves each representing a different. value of another'factor and capable of being inteisected by said last mentioned parallel lines, Vsaid scales and set of curves being suitably located whereby guide lines may be drawn from the z'one of intersection'of the first set of parallels with the first set ofcurves to the .zone ofV intersection of the second set ofparallelsivith the second -set' of curves. l

'2. A computing device comprising|a sheet having inscribed thereon scale ofd lferent values of a knoivn quantity uniforml spaced according to an arithmetical.progression, a series of curves each representing a different value of arknovvn factor and capable of being intersected by a set of parallel lines draivn from said known quantity values, a scale. of unknown quantity values parallelv'ithV the first scale and also uniformly spacedY accord-- ing to an arithinetical progression and to which a series of parallel lines may be drawn ,across the sheet, and another seriesof curves Veach representing a different value of'anotlier factor and capable of being intersected by saidlast mentioned parallel lines, said curves being suitably located vvherebyA lines parallel lwith said scales may be drawn from I the zone of intersection of the first set ofparaljlels with the first set of curves to the ,zone

of intersection of the second set of parallelsV with the second setV of curves, the factor curves of each series havinga common-focus i represented by the zero of one of said pro- 1 gressions. A

A computing device comprising asheet having inscribed thereona linearscalezof different values of' a known quantity uniformly spaced `according to4 an arithmetical progression, a series of curves each'representing a different value of aknownffactor and capable of beingintersected :by Va Vset of parallel lines drawn from `said knoivn quantity scale values, a linearscalefof un- Vknoivn quantity values parallel with the iirstscale and also uniformly spacedaccording to an arithmetical progression and to vwhich also a series of parallel lines'may beV lio' drawn across the sheet, and `parallel :with

theiirst set of parallels, and anotherseries ofcurves eachrepresenting a different value of Yanother' factor and cap able of `beinginter- Y sected Yby Asaid last `mentioned Vparallel ilines,

said scales being suitably locatedWl/iereby guide lines Yparallel yvvith'said linear sca-lcs may be drawn from the zoneof intersection.V

ofthe first set of parallelsrwith theiirstfset of'ccurves to the zone of rintersection of ithe second Vset of parallels with :the Vsecond set Vof curves, the factorcurves of eachfseries being straight and' having a fcnmnmn ffocus, the tivo focibeing locatedat the Zerovalues of theV tivo progressions.-

Y cenare n'siii'iiri. Y' 

